19-Nov.-14: Conservation of Linear and Angular Momentum

PURPOSE: 

To verify that both Linear and Angular Momentum are conserved in a rotational dynamics apparatus.

This will be shown by rolling a small ball down a ramp off the edge of a table. We then practice the kinematics of this trajectory to find the velocity of the ball at the bottom of the ramp using measuring tape and carbon paper. We then place at the bottom of the ramp a ball catcher which will allow the ball to stick at the point of impact. When the ball collides it begins spinning with the ball catcher which is mounted onto a disk. We measure the Angular velocity of the disk after the collision and determine if momentum is conserved.



APPARATUS:








Equipment:

Rotational Dynamics Apparatus
Solid ball - mass = 28.3-g, diameter =19.0-mm
carbon paper
measuring tape
mass to hang on the apparatus to measure the moment of inertia - mass = 24.7-g
torque pulley - radius = 25.0-mm




EXPERIMENT:

1. We began by setting up and measure the necessary dimensions of our apparatus, which included:
   the distance between the top of the ramp and the table top,
   the distance between the bottom of the ramp and the table top,
   the distance between the table top and the ground.
2. We then calculated the moment of inertia of the disk/torque-pulley/ball-catcher by hanging a mass on a string attached to the apparatus and getting the average angular acceleration of the rotation as the mass descends and as it ascends through the graph.
   
   
   
   
   
   
3. After finding the moment of inertia for the disk/torque-pulley/ball-catcher system we calculated the velocity of the ball at the bottom ramp. This was done both theoretically and experimentally. To find it theoretically, we used conservation of energy. To get an experimental value we started by letting the ball shoot off the ramp, from the table to the ground and using carbon paper measured the horizontal distance of the trajectory. Using this new horizontal distance and those values found previously for the various heights, we calculated the velocity at the bottom of the ramp.
   
   

Now that we'd found initial velocity at the bottom of the ramp, the moment of inertia of the apparatus and with known mass of the ball, we calculated what the final rotational velocity of the entire disk/torque-pulley/ball-catcher system along with the ball.



We then compared our calculated value to the experimental value for angular momentum.





CONCLUSION:

The calculated value for the angular velocity was 1.74-rad/s and the experimental value was 1.572-rad/s.

A Great Day for Physics

(11/19/14, 7:09am)